MHB Find Integer Solutions for (A+3B)(5B+7C)(9C+11A)=1357911

  • Thread starter Thread starter anemone
  • Start date Start date
  • Tags Tags
    Integer
anemone
Gold Member
MHB
POTW Director
Messages
3,851
Reaction score
115
Find all integer solutions (if any) for the equation $(A+3B)(5B+7C)(9C+11A)=1357911$.
 
Mathematics news on Phys.org
I would start by finding the prime factors of 1375911 (there are five) then forming all groups of 3 factors.
 
Hi HallsofIvy!

Thanks for your reply. But since this is a challenge question, I hope you know our expectation here is to receive a full solution, no more, no less. (Happy)
 
No solution because

RHS is odd so all factors are odd so each term in the LHS is odd. there are 3 terms on the LHS and so their sum has to be odd.

but sum is 12A + 8B + 16C which is even so impossible
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

Similar threads

Replies
5
Views
2K
Replies
5
Views
2K
Replies
3
Views
1K
Replies
5
Views
1K
Replies
4
Views
1K
Back
Top